Could oil in the water be coming from the cooler/heater tube at the bottom of the radiator. There is no water in the oil, but the water level drops a little every day, and there is sludge in the recovery tank. There are also no leaks of coolant anywhere I can find. HELP!

A bad oil cooler will put oil in the water , but hardly any water may get in the oil. The oil side of a cooler is high pressure , and water side low pressure, thus the transfer. The problem is , your loosing coolant , and you can't see a leak. A bad head gasket can put sludge in the cooling system , and you will loose coolant, (out of the exhaust ) while you are running . But you would normally see higher coolant temps. also. I would pressure test the cooling system , if the pressure drops over time , pull your plugs and see if there is any coolant on any of the pistons. if so the head gasket is bad.... the cooler can of course be pressure tested also..........cheers

Thanks a million Scot. That pretty much answers my suspitions. Incidentally, I'm a tar heel myself, born in Charlotte, raised in Asheville, Raleigh, Rockingham, then as an adult in Raleigh and Wilmington. All my relatives are there.
The coast is my favorite place to be.
Thanks again for the info.

Very nice XJ Larry, if your Jag runs well and there are no signs of burning coolant out back, I would suspect the radiator having corrosion through between the coolant side and oil cooler.
I do think coolant Will get into the oil as it is heavier than oil and there is sufficient pressure to do so when parked and hot. You may simply not be seeing foam under the filler cap yet.
If you haven't already, STOP driving the car. If you are a decent mechanic, do a compression test, look at all spark plugs as others recommend, take off a valve cover and look for foamy signs of coolant in the oil... If everything checks out remove the radiator and have it tested. Maybe you will get lucky and simply have to replace the radiator.
I wish you the best of luck determining this issue,
Regards, Matt